First time using bevel tool, doesn't bevel evenly. What am i doing wrong?
Your object has been scaled in object mode but the transformation has not been applied, so your mesh has a non-uniform scale that will prevent you from doing a clean bevel the way you want it.

Exit Edit mode (Tab) and press CtrlA and apply the scale (you can also use the menu: Object>Apply>Scale).

Back in edit mode the bevel should work evenly centered on the edge...